Problem: All of the 3rd grade teachers and students from Almond went on a field trip to an archaeology museum. Tickets were $$5.00$ each for teachers and $$4.50$ each for students, and the group paid $$28.00$ in total. A few weeks later, the same group visited a science museum where the tickets cost $$20.00$ each for teachers and $$8.50$ each for students, and the group paid $$74.00$ in total. Find the number of teachers and students on the field trips.
Explanation: Let $x$ equal the number of teachers and $y$ equal the number of students. The system of equations is: ${5x+4.5y = 28}$ ${20x+8.5y = 74}$ Solve for $x$ and $y$ using elimination. Multiply the top equation by $-4$ ${-20x-18y = -112}$ ${20x+8.5y = 74}$ Add the top and bottom equations together. $ -9.5y = -38 $ $ y = \dfrac{-38}{-9.5}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $ {5x+4.5y = 28}$ to find $x$ ${5x + 4.5}{(4)}{= 28}$ $5x+18 = 28$ $5x = 10$ $x = \dfrac{10}{5}$ ${x = 2}$ You can also plug ${y = 4}$ into $ {20x+8.5y = 74}$ and get the same answer for $x$ ${20x + 8.5}{(4)}{= 74}$ ${x = 2}$ There were $2$ teachers and $4$ students on the field trips.